Wednesday, August 21, 2013

Is the wavefunction ontological or epistemological?

Part 6: Is the Moon there if we are not looking at it?

What does objective reality mean? Intuitively this is very
clear: the world is out there independent of me, it exists “objectively”. But
is this in agreement with quantum mechanics and with experimental evidence?
Quantum mechanics predicts only the probabilities of experimental outcomes, and
Einstein thought this must mean quantum mechanics is incomplete. By now we know
quantum mechanics is the entire story so how can we reconcile probabilities
with realism? One possible quantum mechanics explanation is the Bohmian
interpretation (http://plato.stanford.edu/entries/qm-bohm/).
Here, particles exists objectively and they are guided by a “quantum potential”
allowing them to move in such a way that they recover the predictions of standard
quantum mechanics.

But wait a minute; didn’t Bell
prove the impossibility of local realism? How can this guiding potential allow
the particle to achieve super-classical correlations, especially when one
particle can be here and the other one at the other end of the galaxy? Simple:
the particles move faster than the speed of light but without being able to
carry signals!! No, no, no, unicorns and Santa Claus you may say. What about an
electron? If the electron is whisked away it should radiate and we should see
this radiation all around us. Also what happens in an atom if the electrons
have definite positions? Would this mean the atom is unstable?

Because in part of the radiation problem there are no known
generalizations of Bohmian mechanics for relativistic quantum field theory, and
very likely there is not possible to obtain one. Also in this interpretation,
the atom consists of stationary electrons at a fixed distance. Not only the
existence of this particular distance is very strange, but also in general the
Bohmian trajectories are known to be “surreal”.

But is there a more formal way to disprove classical realism,
even non-local one? We need to start by the definition of realism. The best
place to start is from EPR’s reality
criterion:

“If without in any way disturbing a system, we
can predict with certainty (i.e. with probability equal to unity) the value of
a physical quantity, then there exists an element of reality corresponding to
that quantity”

So for example, if I measure the position of a particle and
I find a definite value, measuring again in quick succession would yield the
same value because “the particle is there”. The reverse implication is given by
EPR realism: if I predict with certainty the
position of the particle (and any measurement would confirm my prediction) then
the particle must really be there.

We can now prove that EPR’s
reality criterion is actually inconsistent with quantum mechanics, and to do
this we will reason very similarly with Bell
from his famous theorem.

The gist is as follows: we will consider a quantum system
for which we can predict with certainty both an outcome and a correlation. But given
one measurement, a subsequent measurement (in a different configuration) must
respect a quantum mechanics rule and this can be shown to destroy the
correlation. In other words, the law of subsequent measurements, the certainty
of the outcome and the certainty of the correlations are incompatible. So which one should be sacrificed? The law of
subsequent measurements is iron-clad and validated by experiments. Quantum correlations
are indisputable also. What remains is realism. Late Asher Peres use to say: “unperformed
experiments have no results”. But this is stronger. We may say: “unperformed
experiments for which the outcome can be predicted with certainty have no
results”.

Start with a Bell
singlet state: (|+>|-> - |->|+>) and have Alice and Bob measure
this on the vertical axis: one will get spin up and the other one spin down. Supposing
the spins do exists independent of measurement, then they must be oriented on
vertical axis (we don’t know how for each person) to achieve perfect anti-correlation.
[Suppose they are oriented in opposite directions, randomly distributed. Then
the measurement correlation is no longer minus the cosine of the angle between
the measurement axis-as predicted by quantum mechanics and validated by
experiments, but minus 1/3 ofthe
cosine of the angle between the measurement axis]. This may look conspiratorial
(after all we can select any other axis to the same end), but it is an
experimental fact.

Because we can predict with certainty the spin alignment direction,
the alignment direction must really exist by EPR
reality criterion.

But now we can ask if this direction is compatible with Bell
correlation. When measurement directions for Alice and Bob are orthogonal, the
total correlation is zero. Is the vertical axis correlation compatible with
this correlation? The answer is no by an impossible inequality: ¼=0.25 < sin^2(π/8)
≈ 0.1464 (see http://arxiv.org/abs/1211.4270)

There is still a way out however: remember Bohmian mechanics
and non-local realism. Suppose the axis were in a place compatible with the
correlation, but the very act of the intermediate measurement made the axis instantaneously realign. Fortunately
relativity comes to the rescue and proves this is impossible. Why? Because if
Alice and Bob are spacelike separated in
a reference frame Alice does her measurement first and realigns the axis on her
measurement direction, and in another Bob does his measurement first and
realigns the axis on his direction. And the spin direction cannot have two
values at the same time. The only way out is to conclude EPR realism is false.

But what about the Moon then? The Moon is there even when we don’t look at it because of decoherence: the moon is “observed” by the
solar wind, cosmic radiation, etc, so someone is constantly looking at it!

And what about Bohmian mechanics? Would this argument not
disprove this interpretation as well? Nope, because ve…eery conveniently, spin
is not (cannot be) treated classically in this interpretation.